Group action invariants
| Degree $n$ : | $20$ | |
| Transitive number $t$ : | $341$ | |
| Parity: | $1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,15,17,5,10,4,13,19,8,11)(2,16,18,6,9,3,14,20,7,12), (1,9,8,19,14,2,10,7,20,13)(3,11,6,18,15,4,12,5,17,16), (1,16,17,6,9,4,14,19,7,12)(2,15,18,5,10,3,13,20,8,11) | |
| $|\Aut(F/K)|$: | $4$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 3 4: $C_2^2$ 5: $C_5$ 10: $C_{10}$ x 3 20: 20T3 80: $C_2^4 : C_5$ x 17 160: $C_2 \times (C_2^4 : C_5)$ x 51 320: 20T72 x 17 1280: 20T190 2560: 20T263 x 3 Resolvents shown for degrees $\leq 23$
Subfields
Degree 2: None
Degree 4: None
Degree 5: $C_5$
Degree 10: $C_2 \times (C_2^4 : C_5)$ x 3
Low degree siblings
20T341 x 12239Siblings are shown with degree $\leq 23$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 224 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $5120=2^{10} \cdot 5$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |